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Yu-Ru Liu
2014-09-19 ~ 2015-01-16
10:00:00 - 11:30:00
103 , Mathematics Research Center Building (ori. New Math. Bldg.)

Objective: The course is an introduction to the use of analytic methods in the study of Diophantine problems. We aim to cover the following topics:
1) Waring's Problem: Weyl's inequality, Hua's lemma, singular integral, singular series.
2) Vinogradov's Methods: Vinogradov's mean value theorem, large sieve inequality, Weyl's shift, Wooley's efficient congruencing method.
3) Additive Combinatorics: Roth's theorem on 3-term arithmetic progressions, Sarkozy's theorem on difference sets.

References:
1) H. Davenport, Analytic methods for Diophantine equations and Diophantine inequalities, Cambridge Mathematical Library (2005).
2) M. B. Nathanson, Additive number theory - the classical bases, Springer (1996).
3) R. C. Vaughan, The Hardy-Littlewood method, second edition, Cambridge University Press (1997).

Organizer: Jing Yu  ( TIMS & National Taiwan University )